Trudinger-Moser Type Inequality Under Lorentz-Sobolev Norms Constraint  

作　　者：ZHU Maochun ZHENG Yifeng 

机构地区：[1]School of Mathematical Sciences,Institute of Applied System Analysis,Jiangsu University,Zhenjiang 212013,China

出　　处：《Journal of Partial Differential Equations》2021年第2期116-128,共13页偏微分方程（英文版）

摘　　要：In this paper,we are concerned with a sharp fractional Trudinger-Moser type inequality in bounded intervals of IR under the Lorentz-Sobolev norms constraint.For any 1<q<∞andβ≤(√π)q'≡βq'q'=q/q-1,we obtain u∈Н1/2,2(I),^sup||(-△)1/4u||2,q≤1^(∫Ieβ|u(x)|q'dx≤c0|I|),andβq is optimal in the sense that u∈Н1/2,2(I),^sup||(-△)1/4u||2,q≤1^(∫Ieβ|u(x)|q'dx+∞),for anyβ>βq.Furthermore,when q is even,we obtain u∈Н1/2,2(I),^sup||(-△)1/4u||2,q≤1^(∫Ih(u)eβq|u(x)|q')dx≤+∞),for any function h:[0,∞→[0,∞)with lim t→∞h(t)=∞.As for the key tools of proof,we use Green functions for fractional Laplace operators and the rearrangement of a convolution to the rearrangement of the convoluted functions.

关 键 词：Trudinger-Moser inequality Lorentz-Sobolev space bounded intervals 

分 类 号：O17[理学—数学]